Asymptotic behavior of solutions of third-order nonlinear dynamic equations on time scales

In this paper, we will study asymptotic behavior of solutions to third-order nonlinear dynamic equations on time scales of the form ( 1 a 2 ( t ) ( ( 1 a 1 ( t ) ( x Δ ( t ) ) α 1 ) Δ ) α 2 ) Δ + q ( t ) f ( x ( t ) ) = 0 . By using the Riccati technique and integral averaging technique, two different types of criteria are established, one of which extends some existing results and the other is new. Two examples of dynamic equations on different time scales are given to show the applications of the obtained results.